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The worksheet requires factoring out the greatest common factor (GCF) from the given algebraic expressions. Let's go through each problem and solve them by factoring out the GCF:

1. \( 36x^2 - 24x \)
   - The GCF of \( 36x^2 \) and \( 24x \) is \( 12x \).
   - Factored form: \( 12x(3x - 2) \)

2. \( 8x - 12 \)
   - The GCF of \( 8x \) and \( 12 \) is \( 4 \).
   - Factored form: \( 4(2x - 3) \)

3. \( 40x^3 - 48x^7 \)
   - The GCF of \( 40x^3 \) and \( 48x^7 \) is \( 8x^3 \).
   - Factored form: \( 8x^3(5 - 6x^4) \)

4. \( 4x^3 - 21x^2 \)
   - The GCF of \( 4x^3 \) and \( 21x^2 \) is \( x^2 \).
   - Factored form: \( x^2(4x - 21) \)

5. \( 20x^2 + 14x + 12 \)
   - The GCF of \( 20x^2 \), \( 14x \), and \( 12 \) is \( 2 \).
   - Factored form: \( 2(10x^2 + 7x + 6) \)

6. \( 60x^2y^3z^6 - 15xy^{14}z^3 - 45x^7z^5 \)
   - The GCF of these terms is \( 15x \).
   - Factored form: \( 15x(4xy^3z^6 - y^{14}z^3 - 3x^6z^5) \)

7. \( 35x^2y^3z^7 + 15xy^4z^3 - 40x^7y^2 \)
   - The GCF of these terms is \( 5x \).
   - Factored form: \( 5x(7xy^3z^7 + 3y^4z^3 - 8x^6y^2) \)

Would you like more details on any of the steps, or explanations on how to factor out the GCF?

Here are 5 related questions to consider:
1. How do you determine the GCF of two or more terms?
2. Can you factor an expression that has no common factors?
3. How do variables with exponents affect the GCF?
4. What is the process for factoring trinomials?
5. How would you factor expressions involving more than three terms?

**Tip:** Always start by factoring out the greatest common factor (GCF) before attempting more complex factoring methods.

Factor out the GCF from the expression for problems such as 36x^2 - 24x, 8x - 12, and more complex algebraic expressions.

Solve algebraic expressions by factoring out the Greatest Common Factor (GCF). This worksheet includes problems such as 36x^2 - 24x, 8x - 12, and more complex expressions. Suitable for Grades 8-10 students, covering algebra and factoring techniques.

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